We consider a problem of distributed lossy source coding with three jointly Gaussian sources (y1,y2,y3), where y1 and y2 are positively correlated, y3=y1-cy2, c >=0, and the decoder requires reconstructing y3 with a target distortion. Inspired by results from the binary expansion model, the rate-distortion region of this problem is characterized within a bounded gap. Treating each source as a multi-layer input, it is shown that the layers required by the decoder are combined with some unneeded information, referred as interference. Therefore, the responsibility of a source coding algorithm is not only to eliminate the redundancy among the inputs, but also to manage the interference. It is shown that the interference can be effectively managed through some linear operations among the input layers. Binary expansion model demonstrates that some middle layers of y1 and y2 are not needed at the decoder, while some upper and lower layers are required. Structured (Lattice) quantizers enable the encoders to pre-eliminate unnecessary layers. While in the lossless distributed source coding cut-set outer bound is tight, it is shown that in the lossy ones, even for binary expansion models, this outer-bound has an unbounded gap with the rate distortion region. To prove the bounded-gap result, a new outer-bound is established.